Question

A pipeline is to be built to cross a 0.5km wide river and reach a point which is 6km down the river on the opposite bank. it cost 50% more to build across the river than on land. How should the pipeline be routed in order to minimize cost?

Answer 1

c(x) = 1.5m √(x² + 0.5²) + m(6-x), where m is the cost (a constant), where (6-x) is the distance away from the point on the bank.

Graph and x = 1/√(5) will minimize the cost.
6 - 1/√(5) is the distance away from the point on the bank

Answer 2

ok i think i understand what you did. just wondering how you got 1.5

Answer 3

if m is the cost for land then (m + 0.5m) = 1.5m is the cost for water

Answer 4

thanks. this clears things up alot :)